Question

The distance between two planets of masses M and 4M is 'a' what is the gravitational potential at a point on a line joining them of which the gravitational intensity is zero?

• A. $-\frac{9GM}{r}$
• B. $-\frac{5GM}{a}$
• C. $-\frac{3GM}{a}$
• D. $-\frac{7GM}{a}$

Answer 1

The correct option is A $-\frac{9GM}{r}$

Let the point be the position when the gravitational field in zero

$\frac{Gm}{x^2}=\frac{G\left(4m\right)}{(r-x{)}^2}\Rightarrow \frac{1}{x}=\frac{2}{(r-x)}$

$r-2=2xx=r/3$

The point ${}^{\prime }{P}^{\prime }$ is at a distance $\frac{r}{3}$ from man $m$ and $\frac{2r}{3}$ from man $4m$

$\therefore v=\frac{-Gm}{r/3}-\frac{G\left(4m\right)}{\frac{2r}{3}}=\frac{-9Gm}{r}$

$v=\frac{-9Gm}{r}$